It's not the case. All that the document says is that since you
can't distribute a non-free compiler, you just say what compiler
you use and that's enough. The GPL could have made distributing
the compiler a requirement, but that would have so hampered free
software as to make it useless, so the FSF didn't do that.

completely *ignores* the issue of a support API

I think that usually falls under the system software exception
of the GPL. But tricks are played with this. For example, AdaCore
releases their "public GPL" version of their Ada compiler with a
runtime library licensed solely under the GPL, so any programs
built with it that use the runtime can only be distributed as free
software under the GPL. If you pay them for support, they give you
a runtime library licensed under a GPL + program exception rule,
which allows you to distribute it linked into non-free programs.
(All of it is licensed under the GPL, so a paying customer is free
to redistribute it to others, but I doubt any of them bother.)